Bereishit 50:4, after Yaakov's death and mourning, says that Yosef spoke to Paro's house (בֵּית פַּרְעֹה) and asked them to ask Paro for leave so he could go bury his father. During the famine and when Yaakov comes to Mitzrayim we see Yosef address Paro directly, as one would expect from someone in his position.

Why the change here? Perhaps the indirect request is because of something about this specific case (leaving Mitzrayim to bury his father)? Or perhaps, after the famine and the arrival of his family, Yosef didn't have as elevated a position so he needed to go through intermediaries now? Why doesn't he ask Paro directly?

Rashi is silent on this. Someone I study with speculated that after Yosef brought shepherds (who are taboo) to Mitzrayim maybe his relationship with Paro suffered, but he doesn't have a source.

scroll down chabad.org/parshah/in-depth/plainBody_cdo/AID/2710 to 50:6. The talmud Sotah 36b says that pharaoh refused to let yosef bury yaakov until yosef threatened to break an oath he made to pharaoh, never to reveal pharaoh's lack of knowledge of hebrew. It is possible that this is why Yosef initiated the conversation publicly, so that pharaoh couldn't just brush him off.
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MenachemAug 13 '13 at 5:57

The sefer באר יוסף (a sefer I very highly recommend) writes that immediately after Yaakov died the enslavement of Yisrael to Egypt began. This even affected Yosef's elevated status, so much so that he could no longer appeal to Pharaoh directly concerning Yaakov's burial, and instead had to appeal to the members of his household to intercede for him.

Tora Sh'lema cites Tz'ror Hamor as citing a midrash as offering two explanations:

Yosef didn't want to leave his father's side (out of respect for him), so sent messengers instead.

(If I understand it correctly:) Yosef was worried that if he approach Par'o with the request himself then Par'o's people may dissuade Par'o from granting the request. So he got them formally on his side. (I'll include the language of the Tora Sh'lema in case I'm misunderstanding it: "כדי שישאוהו עצה שיניחוהו לעלות שהיה מתיירא מהם שלא יעצוהו שלא לעלות. מתלא אמר קיימון לקטיגורא כי היכא דלא ליטרדך.‏‎")